If two perfect chess AI's played each other, would it always be a stalemate or would white win for an inherent first-move advantage?
This relates to the concept of "solved games". In general, two player turn-based games with perfect information - of which chess is an example - can result in all three possible outcomes: a forced win for white, a forced win for black, or a forced draw.

The short, although unsatisfactory answer is that chess is not solved, and it is not clear whether it can be. There is generally thought to be an advantage to white for the first move, so likely results are considered to be a forced win for white, or a forced draw.

No current AI attempts to "solve" chess, although some of the techniques such as MCTS might be adapted theoretically to find a solution, the available computing power to run that search to completion from the start positions is too low by a few orders of magnitude.